reserve x,N for set,
        k for Nat;
reserve N for with_zero set;
reserve S for IC-Ins-separated non empty with_non-empty_values
     Mem-Struct over N;
reserve s for State of S;
reserve p for PartState of S;

theorem Th16:
 for n being Nat
 holds IC(p +* Start-At( n,S)) =  n
proof
 let n be Nat;
A1: IC S in dom Start-At( n,S) by Th15;
  (Start-At( n,S)).IC S =  n by FUNCOP_1:72;
  hence thesis by A1,FUNCT_4:13;
end;
